Search Results - Numerical methods for ill-posed problems for boundary value problems involving PDEs

Uniqueness and numerical resolution via iterated sensitivity equation of an inverse electromagnetic coefficient problem with partial boundary data

Authors: Heleine, Jérémy

Source: Inverse Problems and Imaging. 19:498-522

Subject Terms: numerical simulations, Inverse problems for PDEs, Maxwell equations, Maxwell's equations, Numerical methods for inverse problems for boundary value problems involving PDEs, inverse problem, uniqueness, sensitivity equation, quasi-reversibility, Numerical methods for ill-posed problems for boundary value problems involving PDEs

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Accurate Adaptive Deep Learning Method for Solving Elliptic Problems: Accurate adaptive deep learning method for solving elliptic problems

Authors: Ying, Jinyong Xie, Yaqi Li, Jiao et al.

Source: Communications in Computational Physics. 37:849-876

Subject Terms: FOS: Computer and information sciences, adaptive sampling method, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), elliptic problems, deep learning methods, Statistics - Computation, Computation (stat.CO), Numerical methods for ill-posed problems for boundary value problems involving PDEs, Artificial neural networks and deep learning

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Access URL: http://arxiv.org/abs/2404.18838

A Direct Sampling Method and Its Integration with Deep Learning for Inverse Scattering Problems with Phaseless Data: A direct sampling method and its integration with deep learning for inverse scattering problems with phaseless data

Authors: Jianfeng Ning Fuqun Han Jun Zou

Source: SIAM Journal on Scientific Computing. 47:C343-C368

Subject Terms: Inverse problems for PDEs, direct sampling method, Numerical methods for inverse problems for boundary value problems involving PDEs, phaseless data, Scattering theory for PDEs, FOS: Mathematics, deep learning, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), inverse scattering problem, Artificial neural networks and deep learning

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Access URL: http://arxiv.org/abs/2403.02584

Continuity-preserved deep learning method for solving elliptic interface problems

Authors: Jiao Li Ran Bi Yaqi Xie et al.

Source: Computational and Applied Mathematics. 44

Subject Terms: Levenberg-Marquardt method, deep learning method, elliptic interface problem, continuity-preserved, Numerical methods for ill-posed problems for boundary value problems involving PDEs, Artificial neural networks and deep learning, convergence analysis

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The time two-grid algorithm combined with difference scheme for 2D nonlocal nonlinear wave equation

Authors: Zhang, Haixiang Jiang, Xiaoxuan Wang, Furong et al.

Source: Journal of Applied Mathematics and Computing. 70:1127-1151

Subject Terms: nonlinear wave equation, two-grid, Boundary value problems for PDEs of mixed type, nonlocal, Boundary element methods for boundary value problems involving PDEs, stability and convergence, Nonlocal and multipoint boundary value problems for ordinary differential equations, Numerical methods for ill-posed problems for boundary value problems involving PDEs, existence and uniqueness

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Access URL: https://zbmath.org/7893811
https://doi.org/10.1007/s12190-024-02000-y

A radial basis meshless method for solving inverse boundary value problems

Authors: Jichun Li

Source: Communications in Numerical Methods in Engineering. 20:51-61

Subject Terms: Inverse problems for PDEs, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Numerical methods for inverse problems for boundary value problems involving PDEs, inverse problem, meshless method, Laplace equation, 0101 mathematics, numerical experiments, radial basis function, linear elliptic equations, 01 natural sciences, ill-posed Cauchy problem

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Access URL: https://www.onlinelibrary.wiley.com/doi/abs/10.1002/cnm.653

Direct method of solution for general boundary value problem of the Laplace equation

Authors: Yoko Ohura Kazuei Onishi K. Hayashi

Source: Engineering Analysis with Boundary Elements. 26:763-771

Subject Terms: Inverse problems for PDEs, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Numerical methods for inverse problems for boundary value problems involving PDEs, direct method, Boundary element methods for boundary value problems involving PDEs, Laplace equation, ill-posed problem, 02 engineering and technology, identification of boundary values, variational method, 01 natural sciences, boundary element method, 0203 mechanical engineering, inverse problem, 0101 mathematics

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Access URL: https://zbmath.org/1910168
https://doi.org/10.1016/s0955-7997(02)00047-4
https://www.sciencedirect.com/science/article/abs/pii/S0955799702000474

Two approaches to the problem of defect correction in vector field tomography solving boundary value problems

Authors: Alfred K. Louis Thomas Schuster E. Yu. Derevtsov

Source: Journal of Inverse and Ill-Posed Problems. 12:597-626

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Inverse problems for PDEs, ray transform, Numerical methods for inverse problems for boundary value problems involving PDEs, Neumann problem, Boundary element methods for boundary value problems involving PDEs, Inverse problems in geophysics, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, boundary element method, Boundary value problems for second-order elliptic equations, vector field tomography, inverse problem, 0101 mathematics, Numerical methods for inverse problems for integral equations, Numerical methods for integral transforms, finite difference method, Radon transform, Dirichlet problem

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Access URL: https://zbmath.org/2182349
https://doi.org/10.1515/1569394042545111
https://www.degruyter.com/view/j/jiip.2004.12.issue-6/1569394042545111/1569394042545111.xml

Numerical method for solving a class of nonlinear elliptic inverse problems: Numerical method for solving a class of nonlinear elliptic inverse problems.

Authors: Abdeljalil Nachaoui S. El Hajji M. Essaouini

Source: Journal of Computational and Applied Mathematics. 162:165-181

Subject Terms: Inverse problems for PDEs, convergence, Numerical methods for inverse problems for boundary value problems involving PDEs, elliptic equation, Applied Mathematics, Boundary element methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, stability, numerical results, Nonlinear inverse problem, 01 natural sciences, Iterative method, Computational Mathematics, Nonlinear boundary value problems for linear elliptic equations, nonlinear Cauchy problem, Ill-posed problem, Boundary element method, 0101 mathematics

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Access URL: https://zbmath.org/2032619
https://doi.org/10.1016/j.cam.2003.08.011
https://ui.adsabs.harvard.edu/abs/2004JCoAM.162..165E/abstract
https://core.ac.uk/display/82252403
https://dialnet.unirioja.es/servlet/articulo?codigo=753118
https://www.sciencedirect.com/science/article/abs/pii/S0377042703007313
https://www.sciencedirect.com/science/article/pii/S0377042703007313

A hybrid method for inverse boundary value problems in potential theory

Authors: Chapko, R. Kress, Rainer

Contributors: Chapko, R. Kress, Rainer

Source: Journal of Inverse and Ill-Posed Problems. 13:27-40

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, regularization, Inverse problems for PDEs, Numerical methods for inverse problems for boundary value problems involving PDEs, Newton method, Tikhonov regularization, Laplace equation, 0101 mathematics, 01 natural sciences, Dirichlet problem

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Access URL: https://zbmath.org/2152326
https://doi.org/10.1163/1569394053583711
https://www.degruyter.com/view/j/jiip.2005.13.issue-1/1569394053583711/1569394053583711.xml?lang=en
https://www.degruyter.com/view/j/jiip.2005.13.issue-1/1569394053583711/1569394053583711.xml
https://resolver.sub.uni-goettingen.de/purl?gro-2/121435

Numerical solution of a Cauchy problem for the Laplace equation

Authors: Lars Eldén Fredrik Berntsson

Source: Inverse Problems. 17:839-853

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Cauchy problem, Inverse problems for PDEs, second central finite difference, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, conformal mapping, Numerical methods for inverse problems for boundary value problems involving PDEs, Tikhonov regularization, least squares problem, Laplace equation, ill-posed problem, numerical results, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, fast Fourier transform, 01 natural sciences, inner boundary, Ill-posedness and regularization problems in numerical linear algebra, steady state heat conduction problem, Conformal mappings of special domains, 0101 mathematics, outer boundary, ill-posedness

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Access URL: http://www.diva-portal.org/smash/record.jsf?pid=diva2:268192
http://iopscience.iop.org/article/10.1088/0266-5611/17/4/316/pdf
http://iopscience.iop.org/0266-5611/17/4/316
https://iopscience.iop.org/article/10.1088/0266-5611/17/4/316/meta
http://ui.adsabs.harvard.edu/abs/2001InvPr..17..839B/abstract

Inverse problem – determining unknown distribution of charge density using the dual reciprocity method: Inverse problem -- determing unknown distribution of charge density using the dual reciprocity method

Authors: Dean Ogrizek Mladen Trlep

Source: COMPEL - The international journal for computation and mathematics in electrical and electronic engineering. 23:701-706

Subject Terms: Inverse problems for PDEs, numerical examples, ill-posed linear system, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Numerical methods for inverse problems for boundary value problems involving PDEs, inverse problems, Boundary element methods for boundary value problems involving PDEs, 01 natural sciences, Poisson's equation, Ill-posedness and regularization problems in numerical linear algebra, 0103 physical sciences, Tikhonov algorithm, 0101 mathematics, dual reciprocity method

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Access URL: https://zbmath.org/2112300
https://doi.org/10.1108/03321640410540629
http://www.emeraldinsight.com/doi/ref/10.1108/03321640410540629
https://dialnet.unirioja.es/servlet/articulo?codigo=948919
https://www.emerald.com/insight/content/doi/10.1108/03321640410540629/full/html

A modified Landweber iterative method for solving a class of parameter identification problems

Authors: M. P. Rajan

Source: Journal of Inverse and Ill-posed Problems. 12:655-669

Subject Terms: Hilbert spaces, Inverse problems for PDEs, numerical examples, convergence, Numerical solutions of ill-posed problems in abstract spaces, regularization, Numerical methods for inverse problems for boundary value problems involving PDEs, Numerical solutions to equations with nonlinear operators, source condition, nonlinear inverse problem, Nonlinear ill-posed problems, Numerical solution to inverse problems in abstract spaces, ill-posed problem, 01 natural sciences, parameter identification, Landweber iteration, 0101 mathematics

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Access URL: https://zbmath.org/2182352
https://doi.org/10.1515/1569394042545148
https://www.degruyter.com/view/j/jiip.2004.12.issue-6/1569394042545148/1569394042545148.xml

an alternating method for an inverse cauchy problem: An alternating method for an inverse Cauchy problem

Authors: Abdeljalil Nachaoui M. Jourhmane

Source: Numerical Algorithms. 21(1):247-260

Subject Terms: Cauchy problem, ill-posed boundary value problems, numerical examples, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Numerical methods for inverse problems for boundary value problems involving PDEs, relaxation algorithm, iterative methods, Ill-posed problems for PDEs, Boundary element methods for boundary value problems involving PDEs, electroencephalography, boundary element method

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Access URL: https://zbmath.org/1382966
https://doi.org/10.1023/a:1019134102565

Neural network solution for an inverse problem associated with the Dirichlet eigenvalues of the anisotropic Laplace operator

Authors: Ossandon, Sebastián Reyes, Camilo Reyes-Martínez, Carlos Marat

Source: Articulos_ANID
Agencia Nacional de Investigación y Desarrollo
instacron:ANID
Conicyt_qa
ANID
Computers & Mathematics With Applications
Artículos CONICYT
CONICYT Chile
instacron:CONICYT

Subject Terms: Numerical methods for eigenvalue problems for boundary value problems involving PDEs, anisotropic Laplace operator, 0203 mechanical engineering, inverse problems, finite element method, 0202 electrical engineering, electronic engineering, information engineering, radial basis functions, 02 engineering and technology, Neural networks for/in biological studies, artificial life and related topics, artificial neural networks, Dirichlet eigenvalues, Numerical methods for ill-posed problems for boundary value problems involving PDEs

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Access URL: http://dblp.uni-trier.de/db/journals/cma/cma72.html#OssandonRR16
https://www.sciencedirect.com/science/article/pii/S0898122116303698
https://researchers.unab.cl/es/publications/neural-network-solution-for-an-inverse-problem-associated-with-th
https://www.sciencedirect.com/science/article/abs/pii/S0898122116303698
https://pure.pucv.cl/es/publications/neural-network-solution-for-an-inverse-problem-associated-with-th
https://dblp.uni-trier.de/db/journals/cma/cma72.html#OssandonRR16
https://hdl.handle.net/10533/227887
https://repositorio-qa.anid.cl/handle/10533/227887
http://hdl.handle.net/10533/227887

Preconditioned all-at-once methods for large, sparse parameter estimation problems

Authors: Uri M. Ascher Eldad Haber

Source: Inverse Problems. 17:1847-1864

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Inverse problems for PDEs, Iterative numerical methods for linear systems, ill-conditioned problem, numerical examples, Gauss-Newton method, Krylov method, Numerical methods for inverse problems for boundary value problems involving PDEs, Numerical computation of matrix norms, conditioning, scaling, data fitting, ill-posed problem, 01 natural sciences, regularization, Tikhonov method, preconditioning, conjugate gradient algorithm, inverse problem, 0101 mathematics, parameter estimation

File Description: application/xml

Access URL: https://iopscience.iop.org/article/10.1088/0266-5611/17/6/319
http://ui.adsabs.harvard.edu/abs/2001InvPr..17.1847H/abstract
https://gif.eos.ubc.ca/sites/default/files/HaberAscher_2001a.pdf
http://iopscience.iop.org/article/10.1088/0266-5611/17/6/319/pdf
http://gif.eos.ubc.ca/sites/default/files/HaberAscher_2001a.pdf

Numerical Solution of the Cauchy Problem for the Stationary Schrödinger Equation Using Faddeev's Green Function: Numerical solution of the Cauchy problem for the stationary Schrödinger equation using Faddeev's Green function

Authors: Masaru Ikehata Samuli Siltanen

Source: SIAM Journal on Applied Mathematics. 64:1907-1932

Subject Terms: Cauchy problem, Inverse problems for PDEs, Faddeev's Green function, numerical examples, algorithm, Numerical solutions of ill-posed problems in abstract spaces, regularization, Numerical methods for inverse problems for boundary value problems involving PDEs, electrocardiography, exponentially growing solution, 01 natural sciences, stationary Schrödinger equation, Schrödinger operator, Schrödinger equation, Boundary value problems for second-order elliptic equations, 0101 mathematics

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Access URL: https://zbmath.org/2121990
https://doi.org/10.1137/s0036139903424916
https://epubs.siam.org/doi/pdf/10.1137/S0036139903424916
https://doi.org/10.1137/S0036139903424916
https://dialnet.unirioja.es/servlet/articulo?codigo=1046351
https://dblp.uni-trier.de/db/journals/siamam/siamam64.html#IkehataS04

FREDHOLM NEURAL NETWORKS.

Authors: GEORGIOU, KYRIAKOS SIETTOS, CONSTANTINOS YANNACOPOULOS, ATHANASIOS N.

Source: SIAM Journal on Scientific Computing; 2025, Vol. 47 Issue 4, pC1006-C1031, 76p

Subject Terms: FREDHOLM equations, ARTIFICIAL neural networks, MATHEMATICAL optimization, NUMERICAL analysis, ARTIFICIAL intelligence, DEEP learning, DIFFERENTIAL equations, INVERSE problems

Numerical Solution of the Identification Problem for the Lower Coefficient of an Elliptic Equation: Numerical solution of the identification problem for the lower coefficient of an elliptic equation

Authors: Petr N. Vabishchevich

Source: Differential Equations. 38:1000-1006

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Inverse problems for PDEs, iterative minimization, Numerical methods for inverse problems for boundary value problems involving PDEs, inverse coefficient problem, 01 natural sciences, ill-posed problems, numerical example, Boundary value problems for second-order elliptic equations, 0103 physical sciences, finite-difference problem, second-order elliptic equation, discrepancy functional, gradient methods

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Access URL: https://link.springer.com/article/10.1023/A%3A1021159730597

An inverse dipole source problem in inhomogeneous media: Application to the EEG source localization in neonates: An inverse dipole source problem in inhomogeneous media: application to the EEG source localization in neonates

Authors: Darbas, Marion Diallo, Mohamadou Malal El Badia, Abdellatif et al.

Contributors: Darbas, Marion Diallo, Mohamadou Malal El Badia, Abdellatif et al.

Source: Journal of Inverse and Ill-posed Problems. 27:255-281

Subject Terms: Biomedical imaging and signal processing, Identification in stochastic control theory, Numerical methods for inverse problems for boundary value problems involving PDEs, PDEs in connection with biology, chemistry and other natural sciences, stability, identifiability, 16. Peace & justice, 01 natural sciences, Least squares and related methods for stochastic control systems, inverse source problem, EEG, Sensitivity, stability, well-posedness, 0101 mathematics, numerical experiments, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]

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Access URL: https://zbmath.org/7068273
https://doi.org/10.1515/jiip-2017-0120
http://www.degruyter.com/view/j/jiip.2019.27.issue-2/jiip-2017-0120/jiip-2017-0120.xml